Rosenberg has voiced his frustration after finding himself consigned to the substitutes' bench for the majority of his 15-month spell at The Hawthorns, and Clarke has revealed that the Swedish international could be sold in January.
The 50-year-old told the Express & Star: "Markus works well in training every day but he hasn't had the chances. He has said himself that he is 31 and for the past 14 or 15 months, or however long that he's been here, he hasn't had enough opportunities.
"He's maybe starting to feel that it might be time to move on and I agree with that assessment. But I'm experienced and he's experienced and we both know that in the next 12 games, before we get to the transfer window, things can change."
Rosenberg has failed to score in 31 appearances for the Baggies.